The first algorithmic random number generator was developed in 1946

Computational and biological systems share fundamental principles, like randomness

Proposed by Alan Turing and John von Neumann, the concept originates from how DNA and computers run by executing encoded instructions in parallel. The advent of AI and the temperature parameter has seen neural networks mimic the randomness of protein encoding.

The foundation for computer viruses was published after its creator's death

In the late 1940s, Hungarian American mathematician, scientist, and engineer John von Neumann gave a series of lectures where he explained the theoretical framework for a computer program that could replicate itself—the von Neumann Universal Constructor. His lectures were later compiled and published in 1966, nine years after his death from cancer.

The first computer virus was created by a USC doctoral candidate in 1983

A year after creating malware in a controlled experiment that multiplied until it took over all of a computer's memory, Fred Cohen went public with his research and its risks. He called the self-replicating software a "computer virus," a term Cohen's advisor, Leonard Adleman, coined to describe its infectious behavior. (Some readers may experience a paywall.)

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

A mathematical and visual analysis distinguishing chaos from randomness

Random systems lack any underlying pattern or causal relationships, while chaos is mathematically deterministic because the behavior follows established laws of nature. In 3D plots, chaotic systems produce outputs that approximate a mathematical function, while random points appear as statistical noise.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

The history and operation of SIGABA, the US counterpart of the Nazi Enigma machine

Developed by the US Army and US Navy, over 10,000 of these machines were deployed by the end of World War II to encrypt messages for the armed forces using three series of rotors. The device would continue to be used until the 1950s, while personal computers were shown to possess enough computing power to crack it by 2021.

Claude Shannon, for whom Anthropic's AI tools are named, proved the existence of an unbreakable cipher

In the one-time pad approach, the encryption key is randomly generated and of equal length to the plaintext. This randomness ensures that every possible plaintext is equally likely—RBBHN can mean HELLO, SOLVE, CODES, and so on, using a different key—while matching the message and key lengths prevents the appearance of patterns that can be exploited.

One of the first mechanical calculators—the Pascaline—was built in the 1640s by French mathematician Blaise Pascal to help his father, who worked as a tax collector.

An overview of 12 fundamental types of algorithms and the uses for each

These include search algorithms to quickly process and find important information, cryptographic algorithms to secure communications, randomized algorithms—such as Monte Carlo simulations for estimating probabilities of outcomes—and greedy algorithms, which make optimal choices based on available data in a step-by-step fashion, as seen in navigation apps.

The term 'artificial intelligence' was coined in 1956

Dartmouth professor John McCarthy introduced the term during a summer workshop aimed at exploring how to make machines perform human-like tasks. Two years later, Perceptron Mark I became one of the first neural network machines.

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

An interview with James Yorke, the man who coined the mathematical term 'chaos'

Along with co-author Tien-Yien Li, the former University of Maryland mathematics department chair published the paper, "Period Three Implies Chaos" in 1975. "Chaos" then became the terminological placeholder for systems with sensitive dependence on initial conditions, which had been well known to mathematicians for over a decade.

Before 1932, when particle accelerators were first used for nuclear research, scientists relied on naturally radioactive substances to advance their understanding of the atomic nucleus.

Designed in 1937 by Harvard graduate student Howard H. Aiken, the 'Harvard Calculator' was used by the US Navy to solve advanced physics problems.

The first compiler to facilitate communication with computers was developed by Grace Hopper

The A-0 program linker automatically translated mathematical symbols into machine-readable binary code. Although it took two years for computer executives to get on board with the idea, the technology was foundational to future programming languages that allowed computers to understand commands written in word-based languages.

The first commercially successful calculating machine—the arithmometer—was patented in 1820 but not mass-produced for over three decades, likely because its inventor was focused on his insurance business.

The life of Edward Lorenz, who originally used a seagull in his 'butterfly effect' metaphor

By accidentally finding that rounding one variable to its third decimal place and re-running a weather simulation produced a drastically different two-month forecast, the American mathematician established the field of chaos theory. His paper—"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?"—introduced the well-known metaphor for the behavior of chaotic systems. (Some readers may experience a paywall.)

Before transistors, which regulate the flow of electricity, vacuum tubes—glass tubes containing no gas that resemble light bulbs—served as the electronic switches in computers.

New Yorker John D. Sweeney Jr. was the first to receive a Social Security number

However, Sweeney died in 1974 having never received any benefits. Social Security numbers were first created to help track workers' earnings so Social Security benefits could be correctly administered.

How a competition honoring a king's birthday uncovered history's first chaotic system

A committee established a contest for King Oscar II's 60th birthday, featuring four unsolved problems in mathematics, including one on proving the stability of a system of more than two objects held together by gravity. Focusing on three celestial objects, Henri Poincaré won the prize for his proof, which he later learned was incorrect and, upon correcting it, instead proved these systems to be unstable.

The origin of chaos theory, colloquially known as the 'butterfly effect'

The theory explains that systems following well-understood physical laws can still produce unpredictable outcomes due to small variations in their initial conditions. Originally identified in weather data, elements of chaos have been observed in stock market fluctuations, cardiac arrhythmias, and the evolution of online social movements.

FLOW-MATIC was the first programming language resembling the English language

As part of the team working on UNIVAC—the first commercially produced electronic digital computer in the US—Grace Hopper helped develop the system that enabled nonprogrammers and businesspeople without a strong mathematics background to use the machine effectively, thereby enhancing the computer's commercial viability.

An explanation of Turing machines—the foundations of digital algorithms and computers

The device reads data, overwrites or ignores it, and then moves on to the next piece of data based on a set of programmed rules. By imagining this data as zeros and ones—binary that makes up computer code—Turing machines became the theoretical models for how any algorithm could be run on a computer if the procedure could be coded into a set of digital rules.

How quantum computers can empower Shor's algorithm to break digital encryption

Secure communications largely rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying to divide by every possible one. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but much easier to calculate using the simultaneous computations enabled by quantum superposition.

The work of Claude Shannon, for whom Anthropic's AI chatbot is named

Known as the father of information theory, Claude Shannon applied Boolean algebra—a subset of mathematics that quantifies true or false statements as 1 or 0, respectively—to circuit design to develop the concept of a binary digit. His paper "A Mathematical Theory of Communication" (1948) laid the groundwork for all modern digital systems.

AI models incorporate a randomness parameter when generating responses to prompts

AI models use this parameter to prevent repeated outputs by sometimes choosing less likely next words during sequential generation. However, this randomness—alongside insufficient data and training—may cause hallucinations of incorrect results.

Unsatisfied with the designs provided by an Apple engineer, Steve Jobs designed the original Mac calculator in about 10 minutes.

The first social media platforms date back to the late 1990s, and their algorithms were typically chronological, with entities like MySpace and Facebook feeding users content from the most recent posts to the oldest.

Computer pioneer Alan Turing was also an elite runner

Alan Turing is credited with helping to found modern computer science, in addition to cracking the Nazi code known as Enigma. Beyond these world-historical achievements, the British mathematician also nearly represented his country in the Olympics in the marathon, running just 11 minutes slower than the eventual gold recipient at the 1948 games. Read more on this lesser-known aspect of the man here.

Since computers rely on the distribution of electrons in microchips to represent binary code, cosmic rays and ionizing radiation from radioactive elements can introduce software errors by detaching electrons from atoms.

How George Gallup changed political polling forever

Straw polls had been used in the 19th century, but it wasn't until George Gallup's use of random sampling in 1936 that the art became a science.

Among the smallest mass-produced mechanical calculators in history, the Curta was designed by Austrian engineer Curt Herzstark while imprisoned in a Nazi concentration camp during World War II.

The basis for AI image and video generation was first introduced in 2014

Through generative adversarial networks, the generator (a neural network that creates fictional data) competes against the discriminator (a neural network that assesses the data) to continuously train the former until it can make content indistinguishable from the real thing. Training with unstructured data can enable software to identify characteristics of gender, age, and expression.

Watch how the Enigma machine encrypts messages and learn about its critical design flaw

Using settings selected from a series of rotors and a plugboard that let operators swap letters with any of their choosing, the machine lit up the output letter for each letter typed. While this system could generate messages requiring any of 150 quintillion potential keys, the machine's reflector never encrypted a letter as itself, providing an entry point for exploiting the system.

Before alarm clocks, people relied more heavily on their circadian rhythms, humans hired to wake them, and on tools such as candle clocks that dropped pins in metal trays at roughly set intervals.

The Model K—named for its construction on a kitchen table—was the first electromechanical digital binary adder, which used an electric circuit to provide the sum of a pair of zeroes and ones in binary.

In 2018, it took about 2.3 years to develop a way to exploit a software bug for malicious purposes, but as of 2026, AI tools have reduced this time to about 20 hours.

VisiCalc was the first electronic spreadsheet, released with Apple II's personal computer in 1979

Before 1979, managers were essentially information processors working off paper ledgers. Scenario modeling was slow, manual, and expensive. Companies were understood as organizations that built things with financial analysis as secondary. VisiCalc made calculation so cheap that you could work iteratively, setting out forecasts and tweaking assumptions until you got the answer you wanted. Oks argues It created a new way of seeing the world.

Early 20th-century debates about horses with 'paranormal mathematical abilities' helped shape modern approaches to psychological research.

The Majorana 1 chip may provide quantum computing using geometry-based qubits

Traditional quantum computers are incredibly fragile, with encoded information easily disrupted and requiring significant error correction systems. Microsoft’s approach involves storing data on a surface, which is more stable, but involves an elusive particle first theorized in 1938.

In a standard deck of 52 cards, shuffling produces one of approximately 8.07 × 10⁶⁷ potential card orders—a number about as large as the number of atoms in the Milky Way.

Random lasers can be created from biomaterials, such as peanuts and birch leaves

Rather than creating a narrow beam of light via amplification in an optical cavity, the random laser produces a red glow by scattering photons created in the natural pores of a peanut kernel after it has been injected with a solution of light-generating carbon dots derived from birch leaves.

Nearly 50 years before the first observational evidence, a soldier fighting on the Eastern Front in World War I found a mathematical solution to Einstein's equations that suggested the existence of black holes.

A mathematical breakdown of how RSA encryption uses prime numbers to encrypt data

This form of asymmetric cryptography uses mathematical functions that rely on the product of two large prime numbers. Because traditional computers struggle to factor such products, obtaining the private keys needed to decrypt messages becomes effectively impossible. This security can be reinforced with larger prime numbers, though this makes encryption more computationally taxing.

Explore interactive simulations of strange attractors, the graphs that help visualize chaos

Although simple, linear equations reach an explicit value for a given input, such as *f(x) \= x* + 1 equaling 4 when *x* equals 3, some chaotic, nonlinear systems tend to evolve towards multiple values simultaneously. These simulations allow users to observe the unusual mathematical artifacts created by systems as their outputs evolve toward these distinct values.

The fast Fourier transform breaks down wave signals into discrete components

The algorithm was initially discovered by German mathematician Carl Friedrich Gauss in 1805, but his notes were not found until after his death. Today, FFTs form the basis for most compression software in media and are essential to technologies such as radar, sonar, and telecommunications.

Watch how Sanger sequencing kickstarted the first generation of DNA sequencing

Sanger sequencing is a foundational DNA sequencing technology developed in 1977. The Nobel Prize-winning discovery uses fluorescent dyes at the end of DNA chains, which are sorted by length through electrophoresis, to determine the order of nucleotide bases.

Noise and instability made quantum computing seem out of reach for decades

Recent advances in error suppression, mitigation, and correction are allowing quantum computers to perform practical tasks that challenge classical machines. IBM’s 2016 launch of its first cloud-accessible quantum computer attracted over 22,000 users in its first month alone.

The first interferometric gravitational wave detector was invented in 1972

Robert Weiss completed the designs after his students asked about an earlier apparatus that used stretched aluminum cylinders to detect passing gravitational waves. Unfamiliar with general relativity and hoping to keep the course focused on experimental tests rather than mathematics, Reiss later asked his students to consider his device for homework. (Some readers may experience a paywall.)